Effects of Linear Transformations

Linear Transformations

Learning Objectives

  1. Define a linear transformation
  2. Compute the mean of a transformed variable
  3. Compute the variance of a transformed variable

This section covers the effects of linear transformations on measures of central tendency and variability.

If a variable X has a mean of μ, a standard deviation of σ, and a variance of σ2, then a new variable Y created using the linear transformation

Y = bX + A

will have a mean of bμ+A, a standard deviation of bσ, and a variance of b2σ2.